Separable Commutative Rings in the Stable Module Category of Cyclic Groups

Separable Algebras over Commutative Rings

Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...

Commutative Local Rings of bounded module type

Let R be a local ring of bounded module type. It is shown that R is an almost maximal valuation ring if there exists a non-maximal prime ideal J such that R/J is an almost maximal valuation domain. We deduce from this that R is almost maximal if one of the following conditions is satisfied: R is a Q-algebra of Krull dimension ≤ 1 or the maximal ideal of R is the union of all non-maximal prime i...

Chevalley Groups over Commutative Rings

Commutative Schur rings over symmetric groups II :

We determine the commutative Schur rings over S6 that contain the sum of all the transpositions in S6. There are eight such types (up to conjugacy), of which four have the set of all the transpositions as a principal set of the Schur ring. 2010 MSC: 20C05, 20F55

Category of $H$-groups

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.